No abstract

This paper explores the optimal design of biased contests. A designer imposes an identity‐dependent treatment on contestants that varies the balance of the playing field. A generalized lottery contest typically yields no closed‐form equilibrium solutions, which nullifies the usual implicit programming approach to optimal contest design and limits analysis to restricted settings. We propose an alternative approach that allows us to circumvent this difficulty and characterize the optimum in a general setting under a wide array of objective functions without solving for the equilibrium explicitly. Our technique applies to a broad array of contest design problems, and the analysis it enables generates novel insights into incentive provisions in contests and their optimal design. For instance, we demonstrate that the conventional wisdom of leveling the playing field, which is obtained in limited settings in previous studies, does not generally hold.

Competitive situations resembling contests are ubiquitous in modern economic landscape. In a contest, economic agents expend costly effort to vie for limited prizes, and they are rewarded for “getting ahead” of their opponents instead of their absolute performance metrics. Many social, economic, and business phenomena exemplify such competitive schemes, ranging from college admissions, political campaigns, advertising, and organizational hierarchies, to warfare. The economics literature has long recognized contest/tournament as a convenient and efficient incentive scheme to remedy the moral hazard problem, especially when the production process is subject to random perturbation or the measurement of input/output is imprecise or costly. An enormous amount of scholarly effort has been devoted to developing tractable theoretical models, unveiling the fundamentals of the strategic interactions that underlie such competitions, and exploring the optimal design of contest rules. This voluminous literature has enriched basic contest/tournament models by introducing different variations to the modeling, such as dynamic structure, incomplete and asymmetric information, multi-battle confrontations, sorting and entry, endogenous prize allocation, competitions in groups, contestants with alternative risk attitude, among other things.

We analyze how the life settlement market-the secondary market for life insurance-may affect consumer welfare in a dynamic equilibrium model of life insurance with one-sided commitment and overconfident policyholders. As in Daily et al. (2008) and Fang and Kung (2010), policyholders may lapse their life insurance policies when they lose their bequest motives; but in our model the policyholders may underestimate their probability of losing their bequest motive, or be overconfident about their future mortality risks. For the case of overconfidence with respect to bequest motives, we show that in the absence of life settlement overconfident consumers may buy "too much" reclassification risk insurance for later periods in the competitive equilibrium. In contrast, when consumers are overconfident about their future mortality rates in the sense that they put too high a subjective probability on the low-mortality state, the competitive equilibrium contract in the absence of life settlement exploits the consumer bias by offering them very high face amounts only in the low-mortality state. In both cases, life settlement market can impose a discipline on the extent to which overconfident consumers can be exploited by the primary insurers. We show that life settlement may increase the equilibrium consumer welfare of overconfident consumers when they are sufficiently vulnerable in the sense that they have a sufficiently large intertemporal elasticity of substitution of consumption.